Final answer:
The mass required for a maximum spring compression of 3.50 cm cannot be determined without the spring constant. OPTION A.
Step-by-step explanation:
The question is asking to find the mass required to give a maximum spring compression of 3.50 cm if the initial speed of the block is 1.59 m/s and the mass can be varied. We can use the conservation of energy to solve this. Initially, the block has kinetic energy, which gets converted into potential energy of the spring (spring potential energy) at maximum compression.
The kinetic energy (KE) formula is:
KE = (1/2) * m * v^2
And the potential energy (PE) stored in a compressed or stretched spring is:
PE = (1/2) * k * x^2
Where m is the mass, v is the speed of the block, k is the spring constant, and x is the compression of the spring. Since the problem doesn't provide the spring constant, we cannot calculate the mass without that critical piece of information, and must state that there is not enough information provided to solve the problem.
Therefore, the correct answer to the problem is (a) Not enough information.